Brass instrument to annoy the French (5)
I believe the answer is:
bugle
'brass instrument' is the definition.
(bugle is a type of brass instrument)
'annoy the french' is the wordplay.
'annoy' becomes 'bug' (I've seen this before).
'the french' becomes 'le' ('the' in French).
'bug'+'le'='BUGLE'
'to' is the link.
(Other definitions for bugle that I've seen before include "It's used for military calls" , "Small trumpet; plant" , "A military trumpet" , "Trumpet-like instrument" , "one may have blown it!" .)